A New Set of Improved Value-at-Risk Backtests

Abstract

We propose a new set of formal backtests for VaR-forecasts that significantly improve upon existing backtesting procedures. Our new test of unconditional coverage can be used for both directional and non-directional testing and is thus able to test separately whether a VaR-model is too conservative or underestimates the actual risk exposure. Second, we stress the importance of testing the property of independent and identically distributed (i.i.d.) VaRexceedances and propose a simple approach that explicitly tests for the presence of clusters in VaR-violation processes. Results from a simulation study indicate that our tests significantly outperform competing backtests in several distinct settings. In addition, the empirical analysis of a unique data set consisting of asset returns of an asset manager's portfolios underline the usefulness of our new backtests especially in times of market turmoil.Keywords: Value-at-Risk, backtesting, Monte Carlo simulation.JEL Classification: C52, C53, C58. * We thank Harald Rosenthal of RobinNova GmbH for providing the data set for our empirical application and helpful comments on an earlier version of this paper. Judith Lameyer and Janina Mühlnickel provided outstanding research assistance. A New Set of Improved Value-at-Risk Backtests ABSTRACTWe propose a new set of formal backtests for VaR-forecasts that significantly improve upon existing backtesting procedures. Our new test of unconditional coverage can be used for both directional and non-directional testing and is thus able to test separately whether a VaR-model is too conservative or underestimates the actual risk exposure.Second, we stress the importance of testing the property of independent and identically distributed (i.i.d.) VaRexceedances and propose a simple approach that explicitly tests for the presence of clusters in VaR-violation processes.Results from a simulation study indicate that our tests significantly outperform competing backtests in several distinct settings. In addition, the empirical analysis of a unique data set consisting of asset returns of an asset manager's portfolios underline the usefulness of our new backtests especially in times of market turmoil.

Liquidity-adjusted Intraday Value at Risk modeling and risk management: An application to data from Deutsche Börse

“…The bold entries are the estimation coefficients that are not significantly different from zero and the Ljung-Box statistics that reject the non-correlation in the residuals. The table contains the p-values for Kupiec, Christoffersen, Unconditional coverage, and I.I.D (Ziggel et al (2014)) tests for the stocks SAP, RWE and MRK.…”

“…When the number of hits is less than two, the pvalues are denoted by #. The table contains the p-values for Kupiec and Christoffersen Unconditional coverage, and I.I.D (Ziggel et al (2014)) tests. Intervals are regularly timespaced from 5 minutes to 10 minutes.…”

“…Section 6 applies the econometric model proposed in Section 5 to data for three stocks and reports the estimation results. The model performance is assessed by the Unconditional Coverage test of Kupiec (1995), the Independence test proposed by Christoffersen (1998), and the new backtests of Ziggel et al (2014). In Section 7, we analyze the ex-ante liquidity risk in LIVaR c and compare the proposed LIVaR with other high-frequency risk measures.…”

“…More specifically, it rejects VaR models that generate clustered violations by estimating a first-order Markov chain model on the sequence. The new set of tests proposed byZiggel et al (2014) analyze unconditional coverage and independence by using simulations with i.i.d Bernoulli random variables. One advantage is that the new tests allow for two-sided testing.Table 3reports the p-values for all tests (two-sided testing for unconditional coverage and i.i.d) on simulated data for confidence levels of 95%, 97.5%, 99% and 99.5%.…”

New backtests for unconditional coverage of expected shortfall

“…While there are several formal VaR-backtests (see, eg. Candelon et al, 2011;Berkowitz et al, 2011;Ziggel et al, 2014, for some recently proposed tests), there are only a few studies dealing with ES-backtests (Berkowitz, 2001;Wong, 2008Wong, , 2010Acerbi and Szekely, 2014). Most recently, Du and Escanciano (2015) proposed some backtests for ES forecasts which are easy to implement.…”